Optimization of Price or Demand Function for Maximum Revenue Calculus

Optimization of Time Application: Find the critical numbers and analyses for optimum value
A unique series developed for the students preparing for GCSE Level A and equivalent examination globally. Anil Kumar has shared his knowledge with students who are preparing for GCSE Level A so that they can understand and perform much better.
Absolute Maximum and Absolute minimum value for any function continuous in closed interval [a, b] will always exist at the critical numbers or at the end points.
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[tobiaschapinda]

A Mr. Peterson wants to sell cheese.After a fixed set-up cost of $250,

he can produce the cheese at a cost of $9 per kilogram.He is able to

produce up to 400kg, but he plans to take advance orders and

produce only what he can sell.His market research suggests that the

amount he would be able to sell depends on the price in the following

way:thea mount decreases proportionally with the price;if he

charged $20 per kg he would not sell any, and if the cheese was free

he would ‘sell’ the maximum 400kg that he could produce.What

price per kilogram should the farmer set in order to maximize his

profit?